Ring Inversion Research Articles

One-sided w-core inverses in rings with an involution

This paper contributes to define one-sided versions of ‘w-core inverse’ introduced by the writer. Given any -ring R and , a is called right w-core invertible if there exists some satisfying awxa = a, and . Several characterizations for this type of generalized inverses are given, and it is shown that a is right w-core invertible if and only if a is right -core invertible if and only if there exists a Hermitian element p such that pa = 0 and is right invertible for any integer , in which case, the expression of right w-core inverses is given. Finally, it is proved that right w-core inverses are instances of right inverses along an element, right -inverses and right annihilator -inverses. As an application, the characterization for the Moore–Penrose inverse is given.

Flap Dynamics in Pepsin-Like Aspartic Proteases: A Computational Perspective Using Plasmepsin-II and BACE-1 as Model Systems.

The flexibility of β hairpin structure known as the flap plays a key role in catalytic activity and substrate intake in pepsin-like aspartic proteases. Most of these enzymes share structural and sequential similarity. In this study, we have used apo Plm-II and BACE-1 as model systems. In the apo form of the proteases, a conserved tyrosine residue in the flap region remains in a dynamic equilibrium between the normal and flipped states through rotation of the χ1 and χ2 angles. Independent MD simulations of Plm-II and BACE-1 remained stuck either in the normal or flipped state. Metadynamics simulations using side-chain torsion angles (χ1 and χ2 of tyrosine) as collective variables sampled the transition between the normal and flipped states. Qualitatively, the two states were predicted to be equally populated. The normal and flipped states were stabilized by H-bond interactions to a tryptophan residue and to the catalytic aspartate, respectively. Further, mutation of tyrosine to an amino-acid with smaller side-chain, such as alanine, reduced the flexibility of the flap and resulted in a flap collapse (flap loses flexibility and remains stuck in a particular state). This is in accordance with previous experimental studies, which showed that mutation to alanine resulted in loss of activity in pepsin-like aspartic proteases. Our results suggest that the ring flipping associated with the tyrosine side-chain is the key order parameter that governs flap dynamics and opening of the binding pocket in most pepsin-like aspartic proteases.

The absorption laws for the weighted core inverse in rings

Necessary and sufficient conditions for the absorption laws of the weighted core inverse, and -inverse are investigated in this paper. In addition, mixed absorption laws for , , , and -inverse are considered.

Left core inverses in rings with involution

Left core inverses in rings with involution

Non-conventional hydrogen bonding and dispersion forces that support embedding mesitylgold into a tailored bis(amidine) framework.

A bis(amidine) ligand operates as a molecular lock for two AuMes fragments. The resulting complex retains a flexible double macrocycle with two non-conventional N-H⋯Cipso hydrogen bonds and distinct intramolecular dispersion forces. Instead of unfolding of the double-ring structure through bond rupture in solution, a conformational ring inversion is observed.

From karyotypes to precision genomics in 9p deletion and duplication syndromes.

While 9p deletion and duplication syndromes have been studied for several years, small sample sizes and minimal high-resolution data have limited a comprehensive delineation of genotypic and phenotypic characteristics. In this study, we examined genetic data from 719 individuals in the worldwide 9p Network Cohort: a cohort seven to nine times larger than any previous study of 9p. Most breakpoints occur in bands 9p22 and 9p24, accounting for 35% and 38% of all breakpoints, respectively. Bands 9p11 and 9p12 have the fewest breakpoints, with each accounting for 0.6% of all breakpoints. The most common phenotype in 9p deletion and duplication syndromes is developmental delay, and we identified eight known neurodevelopmental disorder genes in 9p22 and 9p24. Since it has been previously reported that some individuals have a secondary structural variant related to the 9p variant, we examined our cohort for these variants and found 97 events. The top secondary variant involved 9q in 14 individuals (1.9%), including ring chromosomes and inversions. We identified a gender bias with significant enrichment for females (p = 0.0006) that may arise from a sex reversal in some individuals with 9p deletions. Genes on 9p were characterized regarding function, constraint metrics, and protein-protein interactions, resulting in a prioritized set of genes for further study. Finally, we achieved precision genomics in one child with a complex 9p structural variation using modern genomic technologies, demonstrating that long-read sequencing will be integral for some cases. Our study is the largest ever on 9p-related syndromes and provides key insights into genetic factors involved in these syndromes.

Dynamics and Entropy of Cyclohexane Rings Control pH-Responsive Reactivity.

Activation entropy (ΔS‡) is not normally considered the main factor in determining the reactivity of unimolecular reactions. Here, we report that the intramolecular degradation of six-membered ring compounds is mainly determined by the ΔS‡, which is strongly influenced by the ring-flipping motion and substituent geometry. Starting from the unique difference between the pH-dependent degradation kinetics of geometric isomers of 1,2-cyclohexanecarboxylic acid amide (1,2-CHCAA), where only the cis isomer can readily degrade under weakly acidic conditions (pH < 5.5), we found that the difference originated from the large difference in ΔS‡ of 16.02 cal·mol–1·K–1. While cis-1,2-CHCAA maintains a preference for the classical chair cyclohexane conformation, trans-1,2-CHCAA shows dynamic interconversion between the chair and twisted boat conformations, which was supported by both MD simulations and VT-NMR analysis. Steric repulsion between the bulky 1,2-substituents of the trans isomer is one of the main reasons for the reduced energy barrier between ring conformations that facilitates dynamic ring inversion motions. Consequently, the more dynamic trans isomer exhibits much a larger loss in entropy during the activation process due to the prepositioning of the reactant than the cis isomer, and the pH-dependent degradation of the trans isomer is effectively suppressed. When the ring inversion motion is inhibited by an additional methyl substituent on the cyclohexane ring, the pH degradability can be dramatically enhanced for even the trans isomer. This study shows a unique example in which spatial arrangement and dynamic properties can strongly influence molecular reactivity in unimolecular reactions, and it will be helpful for the future design of a reactive structure depending on dynamic conformational changes.

Thiophene-3-carbonyl Chloride

The X-ray structure of the title compound has been determined for the first time. It shows the ring flip disorder common among thiophene-3-carbonyl derivatives and the occurrence of this phenomenon in the structures of such compounds is discussed.

Weighted Moore-Penrose Inverses and Weighted Core Inverses in Rings with Involution

Weighted Moore-Penrose Inverses and Weighted Core Inverses in Rings with Involution

Conformational Analysis of Heparin-Analogue Pentasaccharides by Nuclear Magnetic Resonance Spectroscopy and Molecular Dynamics Simulations.

Elucidation and improvement of the blood coagulant properties of heparin are the focus of intense research. In this study, we performed conformational analysis using nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations on the heparin pentasaccharide analogue idraparinux, its disulfonatomethyl analogue, which features a slightly improved blood coagulation property, and a trisulfonatomethyl analogue, in which the activity has been totally abolished. As the ring conformation of the G subunit has been suggested as a major determinant of the biological properties, we analyzed the sugar ring conformations and dynamics of the interglycosidic linkages. We found that the conformation of the G ring is dominated by the 2SO skewed boat next to the 1C4 chair in all three derivatives. Both the thermodynamics and the kinetics of the conformational states were found to be highly similar in the three derivatives. Molecular kinetic analysis showed that the 2SO skewed boat state of the G ring is equally favorable in the three analogues, resulting in similar 2SO populations. Also, the transition kinetics from the 1C4 chair to the 2SO skewed boat was found to be comparable in the derivatives, which indicates a similar energy barrier between the two states of the G subunit. We also identified a slower conformational transition between the dominant 4C1 chair and the boat conformations on the E subunit. Both G and E ring flips are also accompanied by changes along the interglycosidic linkages, which take place highly synchronously with the ring flips. These findings indicate that conformational plasticity of the G ring and the dominance of the 2SO skewed boat populations do not necessarily warrant the biological activity of the derivatives and hence the impact of other factors also needs to be considered.

Synergy of Solid-State NMR, Single-Crystal X-ray Diffraction, and Crystal Structure Prediction Methods: A Case Study of Teriflunomide (TFM).

In this work, for the first time, we present the X-ray diffraction crystal structure and spectral properties of a new, room-temperature polymorph of teriflunomide (TFM), CSD code 1969989. As revealed by DSC, the low-temperature TFM polymorph recently reported by Gunnam et al. undergoes a reversible thermal transition at −40 °C. This reversible process is related to a change in Z’ value, from 2 to 1, as observed by variable-temperature 1H–13C cross-polarization (CP) magic-angle spinning (MAS) solid-state NMR, while the crystallographic system is preserved (triclinic). Two-dimensional 13C–1H and 1H–1H double-quantum MAS NMR spectra are consistent with the new room-temperature structure, including comparison with GIPAW (gauge-including projector augmented waves) calculated NMR chemical shifts. A crystal structure prediction procedure found both experimental teriflunomide polymorphs in the energetic global minimum region. Differences between the polymorphs are seen for the torsional angle describing the orientation of the phenyl ring relative to the planarity of the TFM molecule. In the low-temperature structure, there are two torsion angles of 4.5 and 31.9° for the two Z’ = 2 molecules, while in the room-temperature structure, there is disorder that is modeled with ∼50% occupancy between torsion angles of −7.8 and 28.6°. These observations are consistent with a broad energy minimum as revealed by DFT calculations. PISEMA solid-state NMR experiments show a reduction in the C–H dipolar coupling in comparison to the static limit for the aromatic CH moieties of 75% and 51% at 20 and 40 °C, respectively, that is indicative of ring flips at the higher temperature. Our study shows the power of combining experiments, namely DSC, X-ray diffraction, and MAS NMR, with DFT calculations and CSP to probe and understand the solid-state landscape, and in particular the role of dynamics, for pharmaceutical molecules.

Generalized Zhou inverses in rings

We introduce and study a new class of generalized inverses in rings. An element a in a ring R has generalized Zhou inverse if there exists such that for some We prove that has generalized Zhou inverse if and only if there exists such that for some Cline’s formula and Jacobson’s lemma for generalized Zhou inverses are established. In particular, the Zhou inverse in a ring is characterized.

Hydrogen Bonds Control Single-Chain Conformation, Crystallinity, and Electron Transport in Isoelectronic Diketopyrrolopyrrole Copolymers

The combination of computational methods and advanced characterization techniques is used to highlight the role of the intramolecular hydrogen bond in thienyldiketopyrrolopyrrole (ThDPPTh) copolymerized with tetrafluorobenzene (F4) to PThDPPThF4. We investigate how the torsion potentials of ThDPPTh and isoelectronic dithiazolyldiketopyrrolopyrrole (TzDPPTz) are influenced by hydrogen bonding and translate into different conformation, molecular, structural, and opto-electronic characteristics. ThDPPTh exhibits N,S-syn orientation in the most stable conformer locked by an intramolecular hydrogen bond. In TzDPPTz, such a hydrogen bond is not possible, which leads to a “ring flip” and makes the N,S-anti conformer most stable. Copolymers with F4, PThDPPThF4 and PTzDPPTzF4, exhibit straight and curved backbones, respectively, but similar chain rigidity. These conformations are experimentally confirmed by local packing motifs from solid-state NMR spectroscopy. The differences in conformation strongly influence the opto-electronic and structural properties. X-ray scattering and atomic force microscopy reveal lamellar morphologies of both PThDPPThF4 and PTzDPPTzF4, but increased long range order, reduced paracrystallinity, and larger domains of the former. In-depth analysis of solid-state NMR spectra allows for obtaining information on absolute degrees of crystallinity, which are substantially higher for PThDPPThF4. These differences in structural properties cause field-effect electron mobilities of PThDPPThF4 to be larger by a factor of 20.

Transition Path Sampling Study of the Feruloyl Esterase Mechanism.

Serine hydrolases cleave peptide and ester bonds and are ubiquitous in nature, with applications in biotechnology, in materials, and as drug targets. The serine hydrolase two-step mechanism employs a serine-histidine-aspartate/glutamate catalytic triad, where the histidine residue acts as a base to activate poor nucleophiles (a serine residue or a water molecule) and as an acid to allow the dissociation of poor leaving groups. This mechanism has been the subject of debate regarding how histidine shuttles the proton from the nucleophile to the leaving group. To elucidate the reaction mechanism of serine hydrolases, we employ quantum mechanics/molecular mechanics-based transition path sampling to obtain the reaction coordinate using the Aspergillus niger feruloyl esterase A (AnFaeA) as a model enzyme. The optimal reaction coordinates include terms involving nucleophilic attack on the carbonyl carbon and proton transfer to, and dissociation of, the leaving group. During the reaction, the histidine residue undergoes a reorientation on the time scale of hundreds of femtoseconds that supports the "moving histidine" mechanism, thus calling into question the "ring flip" mechanism. We find a concerted mechanism, where the transition state coincides with the tetrahedral intermediate with the histidine residue pointed between the nucleophile and the leaving group. Moreover, motions of the catalytic aspartate toward the histidine occur concertedly with proton abstraction by the catalytic histidine and help stabilize the transition state, thus partially explaining how serine hydrolases enable poor nucleophiles to attack the substrate carbonyl carbon. Rate calculations indicate that the second step (deacylation) is rate-determining, with a calculated rate constant of 66 s-1. Overall, these results reveal the pivotal role of active-site dynamics in the catalytic mechanism of AnFaeA, which is likely similar in other serine hydrolases.

Current advances in the application of dynamic NMR studies of DNA/RNA intra–and inter molecular effect on ring inversion rate constants for molecular diagnosis of gum cancer

Current advances in the application of dynamic NMR studies of DNA/RNA intra–and inter molecular effect on ring inversion rate constants for molecular diagnosis of gum cancer

Moore-Penrose inverses in rings and weighted partial isometries in [formula omitted]algebras

We explore the existence of MP-inverse in rings with involution. In addition, we give some equivalent conditions for an element of a C*−algebra to be a weighted-EP element and weighted partial isometry.

The (b, c)-inverse in semigroups and rings with involution

We first prove that if a is both left (b, c)-invertible and left (c, b)-invertible, then a is both (b, c)-invertible and (c, b)-invertible in a *-monoid, which generalizes the recent result about the inverse along an element by L. Wang and D. Mosic [Linear Multilinear Algebra, https://doi.org/10.1080/03081087.2019.1679073 ], under the conditions (ab)* = ab and (ac)* = ac. In addition, we consider that ba is (c, b)-invertible, and at the same time ca is (b, c)-invertible under the same conditions, which extend the related results about Moore-Penrose inverses studied by J. Chen, H. Zou, H. Zhu, and P. Patricio [Mediterr J. Math., 2017, 14: 208] to (b, c)-inverses. As applications, we obtain that under condition (a2)* = a2, a is an EP element if and only if a is one-sided core invertible, if and only if a is group invertible.

Characterizations and representations of left and right hybrid (b, c)-inverses in rings

Let R be an associative ring with unity 1 and let $$a,b,c\in R$$ . In this paper, several characterizations for left and right hybrid (b, c)-inverses of a are derived. Moreover, their formulae are given by regularities of certain elements. Then, we give characterizations of right (b, c)-inverses and right annihilator (b, c)-inverses of the product of three elements. Finally, relations among the right hybrid (b, c)-inverse of paq, the right (qb, c)-inverse of aq and the right annihilator (b, cp)-inverse of aq are given.

The $(j,m)$-core inverse in rings with involution

Let $R$ be a unital ring with involution. The $(j,m)$-core inverse of a complex matrix was extended to an element in $R$. New necessary and sufficient conditions such that an element in $R$ to be $(j,m)$-core invertible are given. Moreover, several additive and product properties of two $(j,m)$-core invertible elements are investigated and a order related to the $(j,m)$-core inverse is introduced.***********************************************************************************************************************************

Regiospecific Synthesis and Structural Studies of 3,5-Dihydro-4H-pyrido[2,3-b][1,4]diazepin-4-ones and Comparison with 1,3-Dihydro-2H-benzo[b][1,4]diazepin-2-ones.

Nine 3,5-dihydro-4H-pyrido[2,3-b][1,4]diazepin-4-ones (17–25), some of which contain fluoro-substituents, have been regiospecifically prepared by reaction of 2,3-diaminopyridines with ethyl aroylacetates. In two cases, open intermediates have been isolated and these are related to the reaction pathway. The X-ray crystal structure of 1-methyl-4-phenyl-3,5-dihydro-4H-pyrido[2,3-b][1,4]diazepin-4-one (23) has been solved (formula, C15H13N3O; crystal system, monoclinic; space group, C2/c). This is an asymmetric unit constituted by a single nonplanar molecule and its conformational enantiomer due to the presence of the seven-membered diazepin-2-one moiety, which introduces a certain degree of torsion in the adjacent pyridine ring. The 1H, 13C, 15N, and 19F NMR spectra were obtained and the chemical shifts, together with those of the previously published 1,3-dihydro-2H-benzo[b][1,4]diazepin-2-ones (1–16), i.e., a total of 544 values, were successfully compared with the chemical shifts calculated at the gauge invariant atomic orbital (GIAO)/Becke, three-parameter, Lee–Yang–Parr (B3LYP)/6-311++G(d,p) level. The seven-membered ring inversion barrier in 5-benzyl-2-phenyl-3,5-dihydro-4H-pyrido[2,3-b][1,4]diazepin-4-one (25) was determined and, in conjunction with the data from the literature, compared with the B3LYP/6-311++G(d,p) computed values. This allowed the determination of several structural effects. The rotation about the exocyclic N1–CR bond was also calculated and its dynamic properties were discussed.